$L^p$ improving multilinear Radon-like transforms

TL;DR

This paper characterizes the conditions under which multilinear Radon-like transforms are bounded between certain Lebesgue spaces, extending previous results by Tao and Wright.

Contribution

It provides a comprehensive characterization of $L^p$ bounds for multilinear Radon-like transforms, generalizing earlier work to a broader class of operators.

Findings

Identifies $k$-tuples $(p_1,...,p_k)$ for boundedness

Extends Tao and Wright's results to multilinear setting

Provides endpoint characterizations

Abstract

We characterize (up to endpoints) the $k$-tuples $(p_1,\ldots,p_k)$ for which certain $k$-linear generalized Radon transforms map $L^{p_1} \times \cdots \times L^{p_k}$ boundedly into $\mathbb R$. This generalizes a result of Tao and Wright.